I personally know someone who has done this. Twice. With the haskama of rabbonim in E”Y.
She didn’t believe she would ever get married (she was around 40), and she wanted children, but she also is frum and would not consider anything that was “nisht kosher.” She asked a shailah of Daas Torah, was told there is no issur, and with a non-Jewish donor in a fertility clinic there was no potential inyan of her children chalilah marrying their own siblings by accident someday. Some years after having both children, she actually met someone and got married a couple of years ago, but too old to have more children at that point. The issur is l’chatchilah to marry a non-Jew, but b’dieved the child born of such a union (if the mom is Jewish), is also Jewish, and there is no taint of mamzerus. Osnat bore a child by Shechem, and that child was married to Yosef.
The bearing of a child out of wedlock, is typically stigmatized because of the non-tzniusdig actions of the mother and father that led to the pregnancy. If no such activity took place, there were no violations of the laws of tznius or taharas hamishpacha.